Question

The watering acidity in a pool is considered normal when the average pH reading of three daily measurements is between 8.2 and 8.5. If the first two pH reading 8.48 and 8.35, find the range of the pH values for the third reading that will result in the acidity level is normal.

Answer 1

Let x be the third pH value. 

Now, it is given that the average pH reading of three daily measurements is between 8.2 and 8.5 

Also, the first two pH readings are 8.48 and 8.35 

Therefore,

8.2 <\(\big(\frac{8.48 + 8.35 + x}{3}\big)\) < 8.5

Multiplying throughout by 3 in the above equation

3(8.2)< \(\big(\frac{8.48 + 8.35 + x}{3}\big)(3)\) < 3(8.5)

24.6 < 8.48 + 8.35 + x < 25.5 

24.6 < 16.83 + x < 25.5 

Subtracting throughout by 16.83 in above equation 

24.6 – 16.83 < 16.83 + x – 16.83 < 25.5 – 16.83 

7.77 < x < 8.67 

Therefore, 

The value of third pH reading ranges from 7.77 to 8.67